Article Cite This: Langmuir XXXX, XXX, XXX−XXX
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Reducing the Bounce Height during Truncated Spherical Drop Impact on a Solid Surface Sungchan Yun* Department of Mechanical Engineering, Korea National University of Transportation, Chungju 27469, Republic of Korea
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S Supporting Information *
ABSTRACT: Controlling drop dynamics on solid surfaces is an important challenge. In many strategies for efficient drop deposition, drop dynamics is generally assumed to be axisymmetrical. We demonstrate shape-dependent impact dynamics that can considerably modify the dynamics by deforming the drop into a truncated spherical shape at the impact moment. Experimental and numerical studies show the exceptional rim dynamics that lead to reduced bounce heights compared with spherical drops. We investigate the impact dynamics of truncated spherical drops as a function of the truncation depth, surface wettability, and impact velocity numerically. The bounce height of the truncated drop reduces by 56% below spherical drops. To elucidate the mechanism for the reduction in the bounce height, we conduct the horizontal and vertical momentum analyses of truncated drops. The truncated drop impact can potentially open up new opportunities for enhancing drop deposition in practical applications, such as surface coating and spray cooling.
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employing flexible substrates.20 The receding contact angle could serve as one of the key wetting factors for drop rebound.21 In addition, active methods for enhancing drop deposition demonstrated the control of mobility of dielectric liquid drops in an electric field22,23 and the control of the contact line of drops with electrowetting.24 The contact line pinning of sprayed drops could increase the residence time on nonwetting surfaces by utilizing the in situ precipitation of polyelectrolytes on the surface.25 Bouncing dynamics and the contact time of drops on superhydrophobic surfaces were fundamentally studied26 and investigated by developing surface morphologies, such as sub-millimeter-scale tapered post arrays and cylindrical surfaces.27−29 The previous methods for the suppression of drop rebound provide an understanding of the role of the modification of chemical composition of liquid and target surface on impact dynamics. However, the performance of the methods would be limited when the combination of liquid and target solid becomes uncontrollable. In many strategies, the impact dynamics is conventionally assumed to be axisymmetric, so the symmetry breaking in the dynamics can potentially open opportunities for altering drop hydrodynamics. Our group suggested shape-dependent impact dynamics, which could considerably modify impact dynamics and reduce the bounce magnitude by deforming the drop into nonaxisymmetric shapes at the impact moment.30−32 The nonaxisymmetry of the initial shape allowed the noncircular spreading and retraction
INTRODUCTION Control of drop deposition on solid surfaces has made great progress in a wide variety of practical applications, such as surface cooling, coating, and agricultural spraying.1−4 In these applications, drops may exhibit various outcomes, including deposition, bouncing, and splashing, which depend on surface wettability, roughness, and temperature of the solid and fluid properties of liquid.5−8 The rebound and splashing affect the efficiency of drop deposition. In particular, the drop rebound is the main limiting factor in enhancing deposition at moderate impact velocities because a rapid rebound on nonwetting surfaces arises during impact of drops with high surface tension and low viscosity.4,6,7 Low retention of sprayed drops on plant leaves during rebound may result in environmental pollution when the liquid contains herbicide or pesticide materials.9−11 Several dimensionless quantities are employed to account for the effect of the fluid and physicochemical properties on the outcome of the impact. Among these quantities, the most important are the followings: Weber number, We = ρDU2/σ; Reynolds number, Re = ρDU/μ; Capillary number, Ca = μU/σ; and Ohnesorge number, Oh = μ/(ρDσ)1/2, where ρ is the density, D is the equilibrium diameter, U is the impact velocity, σ is the surface tension, and μ is the viscosity of the drop. We focused on the reduction of the height of drop rebound at an inertial−capillary impact regime in this work. Our understanding of drop rebound and control of drop deposition has noticeably improved over the last 20 years. Many works have emphasized modifications of chemical characteristics of liquid or target surfaces by adding polymer solutions4,12,13 or surfactants14−16 to liquid, electrically charging drops,17 oscillating target surfaces mechanically,18,19 and © XXXX American Chemical Society
Received: April 25, 2018 Revised: June 2, 2018
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DOI: 10.1021/acs.langmuir.8b01355 Langmuir XXXX, XXX, XXX−XXX
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Langmuir
adjusted the location of the nozzle very slightly toward one tooth, which formed an asymmetrical electric field. When a voltage of 6 to 7 kV was applied between the electrodes for 7−10 ms, the single drop detached from the nozzle and deformed into nonspherical shapes near the ring. In Figure 1c, the three-lobed shape observed at 7.0 ms initiated the drop oscillation, which, in turn, induced truncated spherical shapes shown at 10.7 and 15.0 ms. Impact behaviors were recorded by using a high-speed camera (Fastcam SA3) and analyzed by an image processing. We fabricated Teflon-coated hydrophobic surfaces (AF1601) and measured the equilibrium contact angle of the water drop on the surface as 116 ± 3° by using the sessile drop method. The advancing and receding contact angles were measured as 119 ± 3° and 110 ± 3° by expanding or contracting the sessile drop, respectively. In the simulation, the volume-of-fluid (VOF) method was employed to predict the impact dynamics of truncated drops. Our numerical techniques were based on previous studies that described the simulations of drop impact on solid surfaces by using the VOF method.31,33,34 Water and air were selected as operating liquid and surrounding gas at room temperature, respectively. The geometric model of the truncated drop and the relevant parameters were introduced as shown Figure 1b, where R is the radius and d is the height of the spherical cap. We denoted a truncation depth (α = d/R) as the ratio of the height of the spherical cap to the radius. The volume of the drop of 4 μL remained constant, which was given as V = (π/ 3)(4R3 − 3Rd2 + d3) under 0 ≤ d ≤ (R/2). The computational domain had a mesh size of 50 cells per drop diameter, and the truncated spherical shape was set as an initial liquid phase in the domain. For a convergence of pressure and velocity fields, we chose a time step of 1 μs and normalized residuals 0.40, the truncated drop can provide an efficient way to completely suppress the rebound even at the highest velocity (We = 22). Figure 5b displays snapshots of the impact behavior of the drops with α = 0.3, 0.5 at the lowest velocity (We = 7) and at the highest velocity (We = 22). During the retraction process, D
DOI: 10.1021/acs.langmuir.8b01355 Langmuir XXXX, XXX, XXX−XXX
Article
Langmuir
Figure 6. Horizontal and vertical momentum analyses for the underlying principle of reduction of the bounce magnitude of truncated drops with the truncation depths of (a) α = 0.50, (b) 0.40, and (c) 0.20 at We = 13. The value of p in the certain axis represents the normalized momentum by the initial value of the spherical drop at t = 0. The positive value of p denotes a spreading state, whereas the negative value of p represents a retraction state. The inlets indicate top-view snapshots of the impact behaviors found at corresponding times. (d) Temporal evolution of the vertical momentum (pz) for varying truncation depths (α = 0−0.50). The inlets describe side-view snapshots of drops at 10 ms.
the drop with α = 0.5 retrains more extended widths of the drop in the x axis than the drop with α = 0.3, as commonly observed at t = 3.0−8.0 ms for We = 7 and 22. Interestingly, the liquid alignment at the left side is formed with the extremely long merged rims at We = 22 and α = 0.5. Increasing the width of the rim in the x axis (rx) can augment the asymmetry of the drop hydrodynamics, thereby preventing the formation of a vertical liquid column by driving the kinetic energy transfer between the horizontal axes through shape oscillation and suppressing the increase in the vertical kinetic energy.30,31 Reducing the bounce magnitude can be related to symmetry breakage in the horizontal momentum and suppression of the vertical momentum. To elucidate the mechanism for the reduction in the bounce magnitude, we employed the horizontal and vertical momentum analyses of truncated drops with α = 0.2−0.5 at We = 13, as shown in Figure 6. The normalized momentum (p) denotes the volume integral of the momentum of the certain axis normalized by the initial vertical momentum of the spherical drop (t = 0), where a sign of the momentum is assumed as a positive one for the spreading process and a negative one for the retraction process. The value of p helps us determine the net momentum in a certain axis of the drop. Figure 6a−c shows the temporal evolution of the horizontal and vertical momentum for α = 0.5, 0.4, and 0.2 of the truncated drop, respectively. The images of the insets describe top-view snapshots of the impact behaviors found at
corresponding times. In the spreading process, px is more pronounced than py because of a preferential flow along the x axis, and the difference of the maximum momentum between the x and y axes increases at higher α. Thus the symmetry breaking in the horizontal momentum can be characterized in terms of a ratio of the maximum momentum between the horizontal axes in the spreading process. The ratios are measured as 1.45, 1.33, and 1.08 for α = 0.5, 0.4, and 0.2 of the truncated drop, respectively. In Figure 6a, the px of the high-α drop is in the spreading process until 4.2 ms and then reverses its sign, which indicates the time the drop starts to retract. The intermediate-α and lowα drops reverse their sign of px at 4.0 and 3.8 ms, respectively, as shown in Figure 6b,c. The discrepancy in the switching time is due to the wider spreading of the high-α drop than the low-α drops, thereby leading to the presence of well-aligned liquid at the left side of the x axis. In the retraction process, the maximum values of py are close to −0.28 at ∼5.7 ms, which is commonly observed in Figure 6a−c. By contrast, the maximum values of px are found at 9.5, 9.2, and 5.5 ms for the high-, intermediate-, and low-α drops, respectively. The high-α drop has a significant discrepancy between px and py during the aligning process of liquid (t = 4.0−7.0 ms), thereby alleviating an inward motion of fluid along the x axis and suppressing the formation of the vertical liquid column. The low-α drop shows only a slight discrepancy between px and py during the retraction process, which indicates that the inward E
DOI: 10.1021/acs.langmuir.8b01355 Langmuir XXXX, XXX, XXX−XXX
Article
Langmuir motions along both horizontal axes are mostly used to induce the upward momentum, thereby resulting in the formation of the vertical liquid column that would potentially lead to (partial) rebound. The findings are confirmed by the temporal variation in the vertical momentum for varying truncation depths, as shown in Figure 6d. The value of pz significantly reduces as α increases, thereby lowering the height of the liquid column, as shown in the images of the insets describing sideview snapshots of drops at 10 ms. The asymmetry of the horizontal momentum and the merging process of rims provide a marked pathway for reducing the bounce magnitude. As an additional note, we demonstrated the impact of truncated drops with various densities, surface tensions, and viscosities by employing water/ethanol and water/glycerin mixtures to understand the effects of the liquid properties on the reduction in the bounce height. At low Oh (Oh = 0.003− 0.013), we found the distinct feature of the asymmetric impact dynamics of the truncated drops, such as the merging rim on the left end along the x axis. In addition, the truncated shape had remarkable effects in reducing the bounce height of the pure water drop (Oh = 0.003). By contrast, at high Oh (Oh = 0.29−1.69), the truncated shape with high viscosities only slightly affected the asymmetry impact dynamics. In addition, the temporal variations in bounce heights of highly viscous truncated drops were similar to those of spherical drops. The details of the effects of the liquid properties on the reduction in the bounce height are described in the Supporting Information.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Sungchan Yun: 0000-0002-1599-4226 Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT & Future Planning) (NRF2017R1C1B5017472).
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CONCLUSIONS We studied the impact dynamics of truncated spherical drops on nonwetting surfaces. Experimental and numerical results showed the exceptional spreading and retraction dynamics that led to reduced bounce heights of the truncated drops compared with spherical drops. In particular, the rim dynamics of the truncated drop showed the distinct feature in the retraction process by merging on the left end along the x axis, thereby playing an important role in enhancing drop deposition. We numerically investigated the impact dynamics as a function of a truncation depth, surface wettability, and impact velocity. The bounce magnitudes of drops at α = 0.5 could reduce by 56 and 45% below spherical drops for CA100 and CA150 surfaces, respectively. The drops with α ≥ 0.4 achieved the antirebound during drop impact at We = 7−22, showing that the maximum bounce height was significantly reduced compared with spherical drops because liquid alignment formed at the left side of the x axis. The horizontal and vertical momentum analysis of drops provided us with a quantitative understanding of the symmetry breaking in hydrodynamics and the subsequent reduction in the bounce magnitude. We expect that the impact dynamics of the truncated shape will give us new insight into shape-dependent impact dynamics, such as the rim dynamics and reduction in the bounce magnitude, and help with industrial applications for drop deposition, such as surface coating, spray cooling, and agricultural spraying.
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Effects of the liquid properties on the reduction in the bounce height: various densities, surface tensions, and viscosities (PDF)
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b01355. F
DOI: 10.1021/acs.langmuir.8b01355 Langmuir XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.langmuir.8b01355 Langmuir XXXX, XXX, XXX−XXX
